Vol49,6,2006 1189 ANNALS OF GEOPHYSICS, VOL. 49, N. 6, December 2006 Key words ionosphere-atmosphere interaction – mid-latitude ionosphere – ionospheric disturbances – atmospheric waves 1. Introduction Various processes in the lower-lying layers of the atmosphere, particularly in the troposphere, summarized for simplicity under the term ‘mete- orological processes’, can affect the ionosphere basically through two channels: i) electrical and electromagnetic phenomena, and ii) upward propagating waves in the neutral atmosphere. We treat the latter category, with upward propagating waves in the neutral atmosphere, which are more important from the point of view of energy depo- sition and atmospheric modification than the phe- nomena under (i). Namely we focus on the effects of planetary waves on the ionosphere. Various tropospheric and to a limited extent stratospheric and mesospheric «meteorologi- cal» processes and periodic solar heating and cooling excite waves in the neutral atmosphere. Upward propagating waves in the neutral at- mosphere and their modifications, interactions and modulations affect the ionosphere, when and if they reach it. Those waves are planetary waves, tidal waves, gravity waves, and infra- sonic waves. Most of the ‘meteorological influ- ences’ on the ionosphere arise from the upward propagating gravity, tidal and planetary waves (e.g., Kazimirovsky et al., 2003). The meteoro- logical influences play an important role in the overall ionospheric variability (e.g., Forbes et al., 2000; Rishbeth and Mendillo, 2001). Lašto- Persistence of planetary wave type oscillations in the mid-latitude ionosphere Jan Laštovička, Petra Šauli and Peter Križan Institute of Atmospheric Physics, Academy of Sciences of Czech Republic, Prague, Czech Republic Abstract Planetary wave type oscillations have been observed in the lower and middle atmosphere but also in the iono- sphere, including the ionospheric F2 layer. Here we deal with the oscillations in foF2 analysed for two Japan- ese and two US stations over a solar cycle (1979-1989) with the use of the Morlet and Paul wavelet transforms. Waves with periods near 5, 10 and 16 days are studied. Only events of duration of three wave-cycles and more are considered. The results are compared with the results of a similar analysis made for foF2 and the lower ion- osphere over Europe (Laštovička et al., 2003a,b). The 5-day period wave events display a typical duration of 4 cycles, while the 10- and 16-day wave events are less persistent with typical duration of about 3.5 cycles and rather 3 cycles, respectively, in all three geographic regions. The persistence pattern in terms of number of cy- cles and in terms of number of days is different. In terms of number of cycles, the typical persistence of oscilla- tions decreases with increasing period. On the other hand, in terms of number of days the typical persistence ev- idently increases with increasing period. The spectral distribution of event duration is too broad to allow for a reasonable prediction of event duration. Thus the predictability of the planetary wave type oscillations in foF2 seems to be very questionable. The longitudinal size of the planetary wave type events increases with increasing wave period. The persistence of the planetary wave type events in foF2 and the lower ionosphere is similar in Europe, but the similarity in occurrence of individual events in foF2 and the lower ionosphere is rather poor. Mailing address: Dr. Jan Laštovička, Institute of At- mospheric Physics, Academy of Sciences of Czech Re- public, Bocni II, 14131 Prague, Czech Republic; e-mail: jla@ufa.cas.cz 1190 Jan Laštovička, Petra Šauli and Peter Križan vička (2006) briefly reviewed effects of atmos- pheric waves (planetary, tidal, gravity and infra- sonic) on the ionosphere. Planetary waves (periods of about 2-30 days) are very predominantly of tropospheric origin and can penetrate directly to heights slightly above 100 km. They have to propagate upwards into the F-region ionosphere via an indirect way. Their effects were observed in the lower iono- sphere (e.g., Laštovička et al., 1994), in the ionospheric E region in h’E (e.g., Cavalieri, 1976) and sporadic-E layer (e.g., Haldoupis et al., 2004), and in the F2 region (e.g., Forbes and Zhang, 1997; Altadill and Apostolov, 2001, 2003; Laštovička et al., 2003b; Altadill et al., 2004). Typical planetary wave periods are broad spectral peaks around 2, 5, 10 and 16 (very broad spectral peak) days, but the planetary wave spectrum is very variable and on individ- ual days it can be much different. They roughly correspond to eigenfrequencies of the atmos- phere, which slightly differ for various modes; for instance for the wave with the zonal wave number 1 they attain values of 1.2, 5, 8 and 12 days (these periods are Doppler shifted by the prevailing wind). All planetary wave periods are quasi-periods with the exact period varying within a period range. Amplitudes of planetary waves are unstable, as well; planetary waves typically occur in bursts of a couple of waves. The duration of such wave bursts in the critical frequency of the F2 region, foF2, in other words the persistence of the planetary wave type events, is the main topic of the paper. Laštovička et al. (2003b) made such investigations for four representative European stations listed in table I. The primary aim of this paper is to make such investigations for representative stations from the mid-latitude U.S.A. and Japan in compari- son with our previous results on the persistence of planetary wave events over Europe. It should be mentioned that in the F region it is correct to use the term planetary wave type os- cillations, because not all oscillations in the plan- etary wave period range are related to planetary waves in the neutral atmosphere; some of them are caused by periodic variability of geomagnet- ic activity (e.g., Altadill and Apostolov, 2003). Planetary waves cannot propagate directly to the F2 region heights. They have to propagate indi- rectly via modulation of other agents like upward propagating tides or gravity waves, vertical drifts, or the turbopause height and its properties. Laštovička et al. (2003a) studied the persist- ence of planetary wave events in the lower ion- osphere over Europe. Data and methods used by Laštovička et al. (2003a,b) allow examine the possible similarity of planetary wave type oscillations in the lower ionosphere and foF2, which is the second topic of the paper. The third topic is to use similarity and/or dissimilarity of planetary wave events in foF2 over Europe, Japan and the U.S.A. for rough estimate of the longitudinal size of planetary wave type events. 2. Data and methods As the basic ionospheric parameter we use the main characteristics of the F2 region, the Table I. Co-ordinates of ionospheric stations and missing intervals from period 1979-1989. Station Geographic latitude Geographic longitude Missing intervals Boulder 40.0°N 105.3°W 1982/1983 Wallops Island 37.9°N 75.5°W 1979, 1987/1988, 1988, 1988/89, 1989 Akita 39.7°N 140.1°E 1984/1985, 1988/1989, 1989 Wakkanai 45.4°N 141.7°E 1988/1989 Juliusruh 54.6°N 13.4°E Slough 51.5°N 0.6°W Pru° honice 50.0°N 14.6°E 1988/1989, 1989 Rome 41.8°N 12.5°E 1979 1191 Persistence of planetary wave type oscillations in the mid-latitude ionosphere widely available critical frequency foF2. Data from four representative stations in Europe, two in the U.S.A. and two in Japan are used over the period 1979-1989 (from maximum to maxi- mum of the solar cycle). The co-ordinates of those stations are listed in table I. Noontime (10-14 LT) average values of foF2 are used. Sometimes there are problems with quality and availability of foF2 data with some stations for some periods (e.g., Burešová, 1997). The above stations and the analyzed period were selected with respect to reduction such problems to min- imum. Therefore good quality data with mini- mum gaps are used in the paper. Single data gaps were interpolated with the use of data of the same station at other local times and/or from neighboring stations at the same time, or combination of both, based on availability of data. Nevertheless, some intervals have not been taken into analysis due to more data gaps. The selection of the optimum period was made for European stations, therefore the number of missing data intervals for the US and Japanese stations are larger. For the «vertical» comparison of the plane- tary wave type oscillation events in Europe we need data representing the lower ionosphere. The radio wave absorption measurements ob- tained by the A3 method utilizing the oblique wave propagation are used. Data from two ra- dio paths from central Europe are used. The path Luxembourg-Panská Ves has parameters as follows: f = 6.09 MHz, feq = 2.1-2.2 MHz (equivalent vertical frequency), reflection point 50°04lN, 10°18lE, transmitter-receiver distance 610 km. The path Deutschlandfunk-Panská Ves has different parameters: f = 1539 kHz, feq = 650- 700 kHz, reflection point 50°16lN, 11°47lE, transmitter-receiver distance 390 km. The ab- sorption along the former radio paths is formed very predominantly at altitudes of about 90-100 km, whereas the latter absorption is formed mostly at altitudes of about 85-90 km. As a mathematical tool for the description of the persistence of planetary wave type oscilla- tions within time series of foF we use wavelet analysis (Torence and Compo, 1998; Vidakovic, 1999). The Continuous Wavelet Transform (CWT) is an excellent tool for analysing chang- ing properties of non-stationary signals. In analyses of signals, the wavelet representations allow us to view a time-domain evolution in terms of scale/period components. The CWT is a convolution of the data sequence with scaled and translated version of the mother wavelet. Varying the wavelet scale and translating along the lo- calised time is possible to construct a picture showing both the amplitude of any feature versus the scale/period and how this amplitude varies with time. For a thorough introduction to wavelet transforms, the reader is referred, e.g., to Mallat (1998). The wavelet transform of the data X(t, z) is defined as (2.1) where ψ0(t) is a mother-wavelet. In the present work, we used Morlet and Paul (complex) mother-wavelets, defined as (2.2) (2.3) where param counts the number of oscillations of the (real part of the) wavelet and provides the user with a degree of freedom that can be easi- ly tuned to a given purpose. Wavelets, as build- ing blocs of models, are well localized in both time and scale (period, frequency). As the Paul wavelet decays more quickly in the time-do- main then Morlet, it enables better time local- ization. The greater difference is in frequency/ period domain. For the given count of evident oscillations in the wavelet the Paul wavelet is much less efficient. As a source Matlab code the wavelet software for Morlet wavelet com- putations provided by Torrence and Compo was used. Matlab codes are available at URL: http://paos.colorado.edu/research/wavelets/. Since Laštovička et al. (2003a) used only less suitable Meyer wavelet in analysis of the planetary wave activity in the lower ionosphere, we use for the «vertical» comparison over Eu- N ( ) ( ) ! ! ( )Paul: param t N i it N 2 2 1, ( ) N N N N 0 1ψ π = − = − + ( 2 )exp exp i tπν=Morlet: ( ) param t t 2 2 , / N0 2 1 4 2 2 0 0 ψ πσ σ πσν − = − ] bg l Z!, z0>aduψ( , )X u z=( , , )T a t z a a u t1 X R 0 − b l# 1192 Jan Laštovička, Petra Šauli and Peter Križan rope only the results of the Mayer wavelet transform as published by Laštovička et al. (2003a,b). The Mayer (e.g., Daubechies, 1994) and Morlet wavelet transforms yielded the same statistical characteristics of the planetary wave type event persistence for foF2 over Eu- rope (Laštovička et al., 2003b). Commercial MATLAB-Wavelet software has been used to compute the Meyer wavelet transform. The wavelet analysis is applied to consecu- tive 1-year long intervals, shifted by half a year (January-December 1979, July 1979-June 1980, January-December 1980, etc.). Thus for Slough and Juliusruh we have 21 partly overlapping in- tervals for the period 1979-1989, for other sta- tions a bit less due to data gaps. Only wave events with duration of at least three wave cycles are taken into account. 3. Persistence of planetary wave type events in foF2 Figure 1 presents an example of the normal- ized wavelet power spectrum for the Morlet wavelet transform. The Morlet wavelet trans- form results are evaluated for the normalized ab- solute power, i.e. we search for intervals with values larger than a fixed value. In terms of colours in fig. 1 it means that we consider only intervals with yellow and red colour of the dura- tion of at least three wave cycles. Only results inside of the conus-of-influence (black thin curve) are taken into account. The border effects affect the information out of the thin curve. Even though the values shown in fig. 1 are nor- malized, the way of their interpretation with re- spect to a fixed level is hereafter called «ab- Fig. 1. Planetary wave type activity inferred from foF2 for Akita, 1 July 1981-30 June 1982, Morlet wavelet transform. Top panel: time series of raw foF2 data. Bottom panel: wavelet power spectrum of the planetary wave activity changing by colour from white and black-blue (minimum values) through green to red and black-red (maximum values). Wavelet power spectrum is normalized to 1. 1193 Persistence of planetary wave type oscillations in the mid-latitude ionosphere solute» power. However, the Morlet wavelet transform results are also evaluated in terms of «relative» power, when the seasonally variable level of the background foF2, shown in the top panel, is taken into account. We consider rela- tive intensifications with respect to the vicinity of the events with duration of at least three wave cycles to be planetary wave type events. This al- lows us to compare the results of the relative and absolute power approach to interpretation of the results as it was done for European data by Laštovička et al. (2003b). Figure 2 shows an ex- ample of the results of the Paul wavelet trans- form. The results of the Paul wavelet transform are evaluated in terms of the «absolute» power in the same way as Morlet results. The most pronounced feature of figs. 1 and 2 is a large temporal and partly spectral variability of the planetary wave activity. The migration of periods of planetary wave activity is also well visible. The large temporal variability of plane- tary wave activity has to result in a limited per- sistence of the individual planetary wave events. The statistics of duration of individual events of the enhanced planetary wave activity for all yearly intervals and period bands centred at 5, 10 and 16 days is summarized in tables II, III and IV for Paul transform, «absolute» evaluation, Mor- let transform, «absolute» evaluation and Morlet transform, «relative» evaluation, respectively. The tables present the number of events together with their mean, median and the most often oc- curring number of cycles for individual stations and the average values for all four stations. Tables II-IV reveal for the 5-day wave the typical persistence of well-developed wave events to be of 4 cycles consistently for all three ways of analysis. For the 10-day wave, both the Fig. 2. The same as fig. 1 but for Paul wavelet. 1194 Table II. Statistics of persistence of planetary wave type oscillations in foF2 for stations from the Northern America and Japan based on the Paul wavelet transform («absolute» evaluation). The average values for medi- ans and the most frequent values are presented with a step of 0.5. Station Period (days) Number of events Median value Mean value Most frequent value Boulder 5 24 4 4.3 4 10 15 4 4.0 3.5 16 20 3.5 3.9 3 Wallops Island 5 20 4 4.2 4 10 15 3.5 3.6 3.5 16 16 3.5 3.5 3 Wakkanai 5 15 4 3.9 4 10 12 3.5 4.0 3.5 16 13 3.5 3.5 3 Akita 5 18 4 4.0 4 10 14 3.5 3.8 3 16 15 3.5 3.5 3 Average values 5 19 4 4.1 4 10 14 3.5 3.7 3.5 16 16 3.5 3.6 3 Table III. Statistics of persistence of planetary wave type oscillations in foF2 for stations from the Northern America and Japan based on the Morlet wavelet transform (absolute values). The average values for medians and the most frequent values are presented with a step of 0.5. Station Period (days) Number of events Median value Mean value Most frequent value Boulder 5 45 4 4.4 3 10 33 3.5 4.2 3 16 32 3.5-4 4.9 3 Wallops Island 5 49 4 4.3 3.5 10 31 4 4.5 3.5-4 16 21 5 5.1 3 Wakkanai 5 43 4 4.4 4 10 34 3.5-4 4.7 3.5 16 34 3.5 4.1 3 Akita 5 52 4 4.5 4 10 38 4 4.0 3.5 16 33 4 4.8 3 Average values 5 47 4 4.4 3.5 10 34 4 4.4 3.5 16 30 4 4.7 3 Table IV. Statistics of persistence of planetary wave type oscillations in foF2 for stations from the Northern America and Japan based on the Morlet wavelet transform (relative values). The average values for medians and the most frequent values are presented with a step of 0.5. Station Period (days) Number of events Median value Mean value Most frequent value Boulder 5 85 4 4.2 4 10 59 3.5 4 3 Jan Laštovička, Petra Šauli and Peter Križan 1195 Persistence of planetary wave type oscillations in the mid-latitude ionosphere median values and the most frequent occurrences provide the typical persistence of 3.5 cycles. For the 16-day wave, medians point to a typical per- sistence of 3.5 cycles and the most frequent val- ues reveal a typical persistence of just 3 cycles. Thus the persistence in terms of the number of cycles slightly decreases with increasing period. In terms of days the typical duration is 20 days for T = 5 days, about 35 days for T = 10 days and about 55-60 days for T = 16 days. In other words, the duration of the wave events in terms of days is longer, not shorter for longer periods. The median, mean and most frequent values are mostly very similar for all four stations and in tables II-IV. This means that American and Japanese stations reveal essentially the same sta- tistical characteristics of persistence of the plane- tary wave type events in foF2, and that the «ab- solute» evaluation of the Paul wavelet transforms and the «absolute» and «relative» evaluation of Table V. Statistics of persistence of planetary wave type oscillations in foF2 over Europe based on the Morlet wavelet transform (relative values). The average values for medians and the most frequent values are presented with a step of 0.5. After Laštovička et al. (2003a). Station Period (days) Number of events Median value Mean value Most frequent value Juliusruh 5 45 4 4.5 4 10 39 4 4.0 3+4 16 35 3.5 3.8 3-3.5 Slough 5 37 4 4.3 4 10 29 3.5 3.6 3.5 16 34 3.5 3.6 3-3.5 Pru° honice 5 49 4.5 4.7 4 10 42 4 4.1 3 16 33 3.5 3.8 3 Rome 5 31 4 4.0 3.5-4 10 33 3.5 3.7 3.5 16 25 3 3.5 3 Average values 5 40 4 4.3 4 10 36 3.5-4 3.9 3.5 16 32 3.5 3.7 3 Table IV (continued). Station Period (days) Number of events Median value Mean value Most frequent value 16 42 4 4.8 3 Wallops Island 5 89 4 4.4 4 10 45 3.5 3.9 3.5 16 35 3.5 4.2 3 Wakkanai 5 98 4 4.4 4 10 61 3.5 4.1 3.5 16 35 3.5 3.8 3 Akita 5 106 4 4.5 4 10 55 4 4.1 3.5 16 40 3.5-4 4 3 Average values 5 95 4 4.4 4 10 55 3.5 4 3.5 16 38 3.5 4.2 3 1196 Jan Laštovička, Petra Šauli and Peter Križan the Morlet wavelet transforms yield very similar statistical characteristics of the planetary wave type events. The only substantial difference is in the number of events derived by different methods, as tables II-IV clearly demonstrate. However, it does not affect the statistical characteristics of the persistence. One source of differences be- tween the «absolute» and «relative» evaluation is the existence of relatively long intervals of high but variable activity. Such an interval is evaluated as one event in «absolute» way, but may provide two or even three events in «rela- tive» way due to that internal structure of the in- terval. The different number of identified events for the Morlet wavelet transform compared with the Paul wavelet transform is probably in- fluenced by different mother wavelets. Tables V and VI show statistical characteris- tics of the persistence of the planetary wave type events over Europe obtained with the Morlet wavelet transform. They are either identical with or very slightly larger than such values from the U.S.A. and Japan for all three periods of waves. This means that the statistical characteristics of planetary wave type event persistence are essen- tially the same in all three geographic regions and, thus, may be considered to be representative for middle latitudes of the Northern Hemisphere. 4. Planetary wave type events in foF2 and the lower ionosphere over Europe As for the «vertical» comparison, we can compare the similarity of statistical characteris- tics of persistence of events, and of occurrence of individual planetary wave type events in foF2 and the lower ionosphere in Europe using data and results of Laštovička et al. (2003a,b). The typical persistence of the 5-day wave in foF2 is four wave cycles (Laštovička et al., 2003b). This is slightly less than the typical persistence of 5 cycles for the 5-day wave in the lower iono- sphere (Laštovička et al., 2003a). For the 10-day and 16-day waves, the typical persistence in foF2 and the lower ionosphere is identical. Thus the typical persistence of planetary wave type oscil- lations in the lower ionosphere and foF2 appears to be almost identical. A quite different pattern is provided by com- parison of individual events. The similarity of Table VI. Statistics of persistence of planetary wave type oscillations in foF2 over Europe based on the Mor- let wavelet transform (absolute values). The average values for medians and the most frequent values are pre- sented with a step of 0.5. After Laštovička et al. (2003a). Station Period (days) Number of events Median value Mean value Most frequent value Juliusruh 5 55 4 4.8 4 10 39 4.5 4.6 4.5 16 30+1* 4 4.8 3 Slough 5 52 4.5 4.8 3-4 10 38 4-4.5 4.7 3.5 16 35 4 4.3 3 Pru° honice 5 33 4 4.6 4 10 42 4 4.4 3 16 31 4.5 4.7 4 Rome 5 55 4.5 4.9 3.5-4 10 52 4 4.2 4.5 16 38 4 4.6 4 Average values 5 49 4-4.5 4.8 4 10 43 4 4.4 4 16 34 4 4.6 3.5 1* = ∼220 days long period of persistent occurrence in 1980. 1197 Persistence of planetary wave type oscillations in the mid-latitude ionosphere occurrence of individual events in foF2 and the lower ionosphere is mostly poor, worse than ex- pected from the results of some studies, which compared neutral wind oscillations in the MLT region with oscillations in foF2 or in the radio wave absorption in the lower ionosphere (e.g., Pancheva et al., 1994). The quasi-simultaneous occurrence of events in foF2 and the lower iono- sphere is rare. The reason might be that the ab- sorption fluctuations are related to fluctuations in the prevailing wind (e.g., Pancheva et al., 1989), while those in foF2 seem to be related more to fluctuations in the tidal winds (e.g., Laštovička and Šauli, 1999). The planetary wave type fluc- tuations in the prevailing wind and the tidal wind differ to some extent. Why and to what degree these fluctuations differ should be examined. Another reason of the poor similarity might be the geomagnetic origin of a significant part of planetary wave type fluctuations in foF2 (Al- tadill and Apostolov, 2003), whereas the geo- magnetic activity does not play a role in plane- tary wave type oscillations in the lower iono- sphere (Pancheva et al., 1989). On the other hand, probably not all planetary wave type oscil- lations from the lower ionosphere have chance to be (indirectly) transported to heights of foF2. 5. Longitudinal size of planetary wave events We analysed the planetary wave events for eight stations, which represented Europe, Japan, and the mid-latitude U.S.A. Similarity of occur- rence (in the sense of simultaneous occurrence) of individual planetary wave type events ob- served in these three separated regions makes possible to estimate the longitudinal size of events or at least to put some constraints on that size. Altadill and Apostolov (2003) used another approach and found a typical longitudinal size of the planetary wave type events in foF2 as fol- lows: T = 5-6 days, 80° T = 10 days, 100° T = 16 days,180° with individual events covering up to the whole globe. Our analysis reveals that there is almost no simultaneous occurrence of the T = 5 days events observed in Europe, Japan and US, even though statistical characteristics of their persist- ence are closely similar. Table VII shows an ex- ample of such a T = 5 days event. The event first occurs in US (Wallops), immediately after the end of the event in US it appears in Europe, and a few days after the end of the event in Europe it appears in Japan, which looks like an east- ward propagation of an event of limited longi- tudinal size. However, if we consider the longi- tudinal difference between the regions (sta- tions) and the typical longitudinal size of 80° found by Altadill and Apostolov (2003), the ob- served absence of simultaneous occurrence of wave events coincides with the typical longitu- Table VII. A T = 5 days event and a T = 10 days event, both observed in the second half of 1986, Morlet wavelet transform. Too short means shorter than 3.0 cycles; short bursts means only short, separated bursts occur. Period 5 days 10 days station Days Cycles Duration Days Cycles Duration Juliusruh 300-316 3.2 16 days 245-279 3.4 34 days Slough Too Short 240-283 4.3 43 days Pru°honice 300-316 3.2 16 days 240-281 4.1 41 days Roma Short Weak Too Short Boulder Too Short No Effect Wallops 266-299 6.6 33 days Short Bursts Wakkanai 320-336 3.2 16 days No Rffect Akita 320-335 3.0 15 days No Effect 1198 Jan Laštovička, Petra Šauli and Peter Križan dinal size of such events established by Altadill and Apostolov (2003). We analysed several T = 7 days events. Such events observed at European, Japanese and US stations showed again almost no simultaneous occurrence of individual events. The T = 10 days events also mostly displayed absence of simul- taneous occurrence, as the event shown in table VII, in correspondence to their typical longitu- dinal size of 100° as found by Altadill and Apostolov (2003). On the other hand, a few T = 16 days events, which were studied, revealed much often simul- taneous or partly simultaneous occurrence of wave events between European, US and Japan- ese stations. One such event happened in 1984 with beginning around day 60 and persistence of four wave cycles in Europe (at all four sta- tions), and beginning slightly later and persist- ing again about four wave cycles for Wakkanai, Boulder and Wallops Island (at southernmost Akita persistence shorter than three wave cy- cles). This is consistent with their much larger typical longitudinal size found by Altadill and Apostolov (2003). 6. Discussion We investigate the persistence of planetary wave type oscillations over Europe among oth- ers in order to clarify possible predictability of such oscillations with applications to the pre- dictions of the radio wave propagation condi- tions. For the sake of predictions, not only the typical values of the persistence of planetary wave type events, but also the spectral distribu- tion of persistence of individual events (= event duration) is required. An example of the spec- tral distribution of event duration is shown in fig. 3, which presents for each region one sta- tion. The spectral distribution of event duration is too broad to allow a reasonable prediction of event duration from foF2 measurements them- selves. Moreover, figs. 1 and 2 display many events of duration shorter than three cycles, which is the lower limit of studied events. Thus the predictability of the planetary wave type os- cillations in foF2 from the measurements of fof 2 itself seems to be very questionable. We have to look for other predictors, which is com- plicated due to different physical origin of dif- ferent planetary wave type events. Unfortunate- ly, we will probably be unable to separate pre- dictable planetary wave type events, which mean that they remain a part of the prediction noise. Improvement of the quality of radio wave propagation predictions in such a way seems to be rather impossible, or at least very difficult. Some planetary wave events have sharp onset and end. Then the determination of planetary wave persistence depends on the time/period res- olution of the used wavelet. Shape of selected wavelet influences how the wavelet captures/de- tects each wave-like event. However, the onset and end of most events is not so sharp and the ac- curacy of the determination of onset duration in such cases may be up to a few days, particularly for the «relative» evaluation. Therefore we can consider the accuracy of determination of the typical persistence of planetary wave events to be rather around half a cycle for 5-day waves, and better for longer periods in terms of wave cy- cles. Fig. 3. Spectra of event duration (number of wave cycles) for the 5-day oscillations, Morlet wavelet trans- form for Boulder («absolute» evaluation, solid curve), Akita («relative» evaluation, long-dash curve), and Juliusruh («absolute» evaluation, short-dash curve). 1199 Persistence of planetary wave type oscillations in the mid-latitude ionosphere 7. Conclusions The basic characteristics of the F2 region, the critical frequency foF2, were analyzed for two US stations, Boulder and Wallops Island, two Japanese stations, Akita and Wakkanai, and the results were compared with the results of Laštovička et al. (2003b) for four European sta- tions Juliusruh, Slough, Pru° honice and Rome, and Laštovička et al. (2003a) for the lower ion- osphere above Central Europe. All data were analyzed over the period 1979-1989 (one solar cycle). Noontime average values (10-14 UT) of foF2 were used. The persistence of planetary wave type oscillations at periods near 5, 10 and 16 days and sometimes 7 days was studied with the use of the Paul, Morlet and Meyer wavelet transforms. Only events of duration of three cy- cles and more were considered. The main re- sults are as follows: 1) There is a large temporal and partly spec- tral variability of planetary wave type activity. The migration of periods of planetary wave ac- tivity is also well visible. The large temporal variability of the planetary wave activity results in a limited persistence of the individual plane- tary wave type events. 2) For the 5-day wave, a typical persistence of well-developed wave events in foF2 is 4 wave cycles. For the 10-day wave, it is rather 3.5 wave cycles. For 16 days, the most frequent values provide typical persistence no more than 3 wave cycles. 3) In terms of the number of wave cycles in the planetary wave type events, the persistence decreases towards longer periods. However, the persistence of wave events in terms of days in- creases towards longer periods. 4) The planetary wave type wave persist- ence characteristics for Europe are either iden- tical with or very slightly larger than correspon- ding values from the U.S.A. and Japan. 5) The spectrum of event duration is very broad. The character of the spectrum does not allow us to predict the duration of an event when we observe its beginning or, say, first 2-3 wave cycles. 6) The longitudinal size of the planetary wave type events increases with increasing peri- od, making the 5-day and 10-day period events in Europe, America and Japan essentially dis- similar, and the 16-day oscillations much more similar among the three regions. 7) While the typical persistence of planetary wave type oscillations in foF2 and the lower ionosphere over Europe is similar, the corre- spondence of occurrence of individual events is rather poor. 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